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📐 Mathematics  ·  Straight Lines  ·  JEE

The equation of a line through (1,2) parallel to 3x + 4y = 5 is:

Answer: 3x + 4y = 11.

  • A 3x + 4y = 11
  • B 3x + 4y = 5
  • C 4x + 3y = 10
  • D 3x - 4y = -5

Correct answer: A. 3x + 4y = 11

Explanation: Parallel: same slope. Line is 3x + 4y = k. Substitute (1,2): 3+8 = 11. So 3x + 4y = 11.

Slope as Rise over Runxy(x₁,y₁)(x₂,y₂)run = x₂−x₁rise = y₂−y₁m = rise/run = (y₂−y₁)/(x₂−x₁) = tanθ

The slope of a line is the ratio of vertical change (rise) to horizontal change (run) between any two points on it - equivalently, the tangent of the angle θ the line makes with the positive x-axis.

Concept context

Points, lines, and curves on the Cartesian plane

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